Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex24_Luc06_GM)
The rewrite relation of the following TRS is considered.
|
a__f(b,X,c) |
→ |
a__f(X,a__c,X) |
(1) |
| a__c |
→ |
b |
(2) |
|
mark(f(X1,X2,X3)) |
→ |
a__f(X1,mark(X2),X3) |
(3) |
|
mark(c) |
→ |
a__c |
(4) |
|
mark(b) |
→ |
b |
(5) |
|
a__f(X1,X2,X3) |
→ |
f(X1,X2,X3) |
(6) |
| a__c |
→ |
c |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
a__f(a__c,a__c,a__c) |
|
→
|
a__f(a__c,a__c,c) |
|
→
|
a__f(b,a__c,c) |
|
→
|
a__f(a__c,a__c,a__c) |
|
= |
t3
|
where t3 =
t0